%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG116+4 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:24:14 AM UTC 2025
% Result : Theorem 0.22s 0.51s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14 % Problem : RNG116+4 : TPTP v9.0.0. Released v4.0.0.
% 0.05/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.37 % DateTime : Fri Jun 20 03:26:31 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.22/0.51 % SZS status Theorem
% 0.22/0.51 % SZS output start Proof
% 0.22/0.51 tff(sdtpldt0_type, type, (
% 0.22/0.51 sdtpldt0: ( $i * $i ) > $i)).
% 0.22/0.51 tff(sdtasdt0_type, type, (
% 0.22/0.51 sdtasdt0: ( $i * $i ) > $i)).
% 0.22/0.51 tff(tptp_fun_W0_39_type, type, (
% 0.22/0.51 tptp_fun_W0_39: $i)).
% 0.22/0.51 tff(xb_type, type, (
% 0.22/0.51 xb: $i)).
% 0.22/0.51 tff(tptp_fun_W0_38_type, type, (
% 0.22/0.51 tptp_fun_W0_38: $i)).
% 0.22/0.51 tff(xa_type, type, (
% 0.22/0.51 xa: $i)).
% 0.22/0.51 tff(xu_type, type, (
% 0.22/0.51 xu: $i)).
% 0.22/0.51 tff(xl_type, type, (
% 0.22/0.51 xl: $i)).
% 0.22/0.51 tff(xk_type, type, (
% 0.22/0.51 xk: $i)).
% 0.22/0.51 tff(aElement0_type, type, (
% 0.22/0.51 aElement0: $i > $o)).
% 0.22/0.51 tff(aElementOf0_type, type, (
% 0.22/0.51 aElementOf0: ( $i * $i ) > $o)).
% 0.22/0.51 tff(slsdtgt0_type, type, (
% 0.22/0.51 slsdtgt0: $i > $i)).
% 0.22/0.51 tff(1,plain,
% 0.22/0.51 (?[W0: $i] : (aElement0(W0) & (sdtasdt0(xb, W0) = xl)) <=> ?[W0: $i] : (aElement0(W0) & (sdtasdt0(xb, W0) = xl))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(2,axiom,((((?[W0: $i] : (aElement0(W0) & (sdtasdt0(xa, W0) = xk)) & aElementOf0(xk, slsdtgt0(xa))) & ?[W0: $i] : (aElement0(W0) & (sdtasdt0(xb, W0) = xl))) & aElementOf0(xl, slsdtgt0(xb))) & (xu = sdtpldt0(xk, xl))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2456')).
% 0.22/0.51 tff(3,plain,
% 0.22/0.51 (((?[W0: $i] : (aElement0(W0) & (sdtasdt0(xa, W0) = xk)) & aElementOf0(xk, slsdtgt0(xa))) & ?[W0: $i] : (aElement0(W0) & (sdtasdt0(xb, W0) = xl))) & aElementOf0(xl, slsdtgt0(xb))),
% 0.22/0.51 inference(and_elim,[status(thm)],[2])).
% 0.22/0.51 tff(4,plain,
% 0.22/0.51 ((?[W0: $i] : (aElement0(W0) & (sdtasdt0(xa, W0) = xk)) & aElementOf0(xk, slsdtgt0(xa))) & ?[W0: $i] : (aElement0(W0) & (sdtasdt0(xb, W0) = xl))),
% 0.22/0.51 inference(and_elim,[status(thm)],[3])).
% 0.22/0.51 tff(5,plain,
% 0.22/0.51 (?[W0: $i] : (aElement0(W0) & (sdtasdt0(xb, W0) = xl))),
% 0.22/0.51 inference(and_elim,[status(thm)],[4])).
% 0.22/0.51 tff(6,plain,
% 0.22/0.51 (?[W0: $i] : (aElement0(W0) & (sdtasdt0(xb, W0) = xl))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.22/0.51 tff(7,plain,(
% 0.22/0.51 aElement0(W0!39) & (sdtasdt0(xb, W0!39) = xl)),
% 0.22/0.51 inference(skolemize,[status(sab)],[6])).
% 0.22/0.51 tff(8,plain,
% 0.22/0.51 (sdtasdt0(xb, W0!39) = xl),
% 0.22/0.51 inference(and_elim,[status(thm)],[7])).
% 0.22/0.51 tff(9,plain,
% 0.22/0.51 (?[W0: $i] : (aElement0(W0) & (sdtasdt0(xa, W0) = xk)) <=> ?[W0: $i] : (aElement0(W0) & (sdtasdt0(xa, W0) = xk))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(10,plain,
% 0.22/0.51 (?[W0: $i] : (aElement0(W0) & (sdtasdt0(xa, W0) = xk)) & aElementOf0(xk, slsdtgt0(xa))),
% 0.22/0.51 inference(and_elim,[status(thm)],[4])).
% 0.22/0.51 tff(11,plain,
% 0.22/0.51 (?[W0: $i] : (aElement0(W0) & (sdtasdt0(xa, W0) = xk))),
% 0.22/0.51 inference(and_elim,[status(thm)],[10])).
% 0.22/0.51 tff(12,plain,
% 0.22/0.51 (?[W0: $i] : (aElement0(W0) & (sdtasdt0(xa, W0) = xk))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[11, 9])).
% 0.22/0.51 tff(13,plain,(
% 0.22/0.51 aElement0(W0!38) & (sdtasdt0(xa, W0!38) = xk)),
% 0.22/0.51 inference(skolemize,[status(sab)],[12])).
% 0.22/0.51 tff(14,plain,
% 0.22/0.51 (sdtasdt0(xa, W0!38) = xk),
% 0.22/0.51 inference(and_elim,[status(thm)],[13])).
% 0.22/0.51 tff(15,plain,
% 0.22/0.51 (sdtpldt0(sdtasdt0(xa, W0!38), sdtasdt0(xb, W0!39)) = sdtpldt0(xk, xl)),
% 0.22/0.51 inference(monotonicity,[status(thm)],[14, 8])).
% 0.22/0.51 tff(16,plain,
% 0.22/0.51 (sdtpldt0(xk, xl) = sdtpldt0(sdtasdt0(xa, W0!38), sdtasdt0(xb, W0!39))),
% 0.22/0.51 inference(symmetry,[status(thm)],[15])).
% 0.22/0.51 tff(17,plain,
% 0.22/0.51 ((xu = sdtpldt0(xk, xl)) <=> (xu = sdtpldt0(xk, xl))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(18,plain,
% 0.22/0.51 (xu = sdtpldt0(xk, xl)),
% 0.22/0.51 inference(and_elim,[status(thm)],[2])).
% 0.22/0.51 tff(19,plain,
% 0.22/0.51 (xu = sdtpldt0(xk, xl)),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.22/0.51 tff(20,plain,
% 0.22/0.51 (xu = sdtpldt0(sdtasdt0(xa, W0!38), sdtasdt0(xb, W0!39))),
% 0.22/0.51 inference(transitivity,[status(thm)],[19, 16])).
% 0.22/0.51 tff(21,plain,
% 0.22/0.51 (^[W0: $i, W1: $i] : refl(((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))) <=> ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(22,plain,
% 0.22/0.51 (![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))) <=> ![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[21])).
% 0.22/0.51 tff(23,plain,
% 0.22/0.51 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite((aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))) <=> (~((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))))), ((~(aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))) <=> (~(~((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))))))), rewrite((~(~((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))))) <=> ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))), ((~(aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))) <=> ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(24,plain,
% 0.22/0.51 (![W0: $i, W1: $i] : (~(aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))) <=> ![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[23])).
% 0.22/0.51 tff(25,plain,
% 0.22/0.51 ((~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))) <=> (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(26,plain,
% 0.22/0.51 ((~?[W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))) <=> (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(27,axiom,(~?[W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.22/0.51 tff(28,plain,
% 0.22/0.51 (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.22/0.51 tff(29,plain,
% 0.22/0.51 (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.22/0.51 tff(30,plain,
% 0.22/0.51 (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.22/0.51 tff(31,plain,
% 0.22/0.51 (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.22/0.51 tff(32,plain,
% 0.22/0.51 (^[W0: $i, W1: $i] : refl($oeq((~(aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))), (~(aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(33,plain,(
% 0.22/0.51 ![W0: $i, W1: $i] : (~(aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))),
% 0.22/0.51 inference(nnf-neg,[status(sab)],[31, 32])).
% 0.22/0.51 tff(34,plain,
% 0.22/0.51 (![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[33, 24])).
% 0.22/0.51 tff(35,plain,
% 0.22/0.51 (![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[34, 22])).
% 0.22/0.51 tff(36,plain,
% 0.22/0.51 (aElement0(W0!39)),
% 0.22/0.51 inference(and_elim,[status(thm)],[7])).
% 0.22/0.51 tff(37,plain,
% 0.22/0.51 (aElement0(W0!38)),
% 0.22/0.51 inference(and_elim,[status(thm)],[13])).
% 0.22/0.51 tff(38,plain,
% 0.22/0.51 (((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))) | ((~aElement0(W0!38)) | (~aElement0(W0!39)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0!38), sdtasdt0(xb, W0!39)))))) <=> ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))) | (~aElement0(W0!38)) | (~aElement0(W0!39)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0!38), sdtasdt0(xb, W0!39)))))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(39,plain,
% 0.22/0.52 (((~aElement0(W0!39)) | (~aElement0(W0!38)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0!38), sdtasdt0(xb, W0!39))))) <=> ((~aElement0(W0!38)) | (~aElement0(W0!39)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0!38), sdtasdt0(xb, W0!39)))))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(40,plain,
% 0.22/0.52 (((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))) | ((~aElement0(W0!39)) | (~aElement0(W0!38)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0!38), sdtasdt0(xb, W0!39)))))) <=> ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))) | ((~aElement0(W0!38)) | (~aElement0(W0!39)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0!38), sdtasdt0(xb, W0!39))))))),
% 0.22/0.52 inference(monotonicity,[status(thm)],[39])).
% 0.22/0.52 tff(41,plain,
% 0.22/0.52 (((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))) | ((~aElement0(W0!39)) | (~aElement0(W0!38)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0!38), sdtasdt0(xb, W0!39)))))) <=> ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))) | (~aElement0(W0!38)) | (~aElement0(W0!39)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0!38), sdtasdt0(xb, W0!39)))))),
% 0.22/0.52 inference(transitivity,[status(thm)],[40, 38])).
% 0.22/0.52 tff(42,plain,
% 0.22/0.52 ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))) | ((~aElement0(W0!39)) | (~aElement0(W0!38)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0!38), sdtasdt0(xb, W0!39)))))),
% 0.22/0.52 inference(quant_inst,[status(thm)],[])).
% 0.22/0.52 tff(43,plain,
% 0.22/0.52 ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))) | (~aElement0(W0!38)) | (~aElement0(W0!39)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0!38), sdtasdt0(xb, W0!39))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.22/0.52 tff(44,plain,
% 0.22/0.52 (~(xu = sdtpldt0(sdtasdt0(xa, W0!38), sdtasdt0(xb, W0!39)))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[43, 37, 36, 35])).
% 0.22/0.52 tff(45,plain,
% 0.22/0.52 ($false),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[44, 20])).
% 0.22/0.52 % SZS output end Proof
% 0.22/0.52 % E exiting
%------------------------------------------------------------------------------